Kuga Yuma does not get Replica back in the World Trigger manga as of chapter 206. However, he will get his chaperone (Replica) back in one piece by the end of Aftokrator away mission.

Can Yuma use his Black Trigger without replica?

They can be used even when Yūma is in a trion body created by another Trigger. Yet another singular characteristic of Yūma's Black Trigger is that its seals can also be used independently by Replica, a Trion Soldier, as well as its small avatars.

Did Jin give up his Black Trigger?

During the skirmish over Yūma's Black Trigger, both combatants joyfully reminisced over the opportunity to fight again. Upon Jin giving up his Black Trigger (and thus his S-Rank status), Tachikawa felt euphoric over the chance to duel him again, and Jin has made it his objective to take Tachikawa's position as the no.